Extension complexity of independent set polytopes
We exhibit an n-node graph whose independent set polytope requires extended formulations of size exponential in Ω(n/log n). Previously, no explicit examples of n-dimensional 0/1-polytopes were known with extension complexity larger than exponential in Θ(n). Our construction is inspired by a relatively little-known connection between extended formulations and (monotone) circuit depth.
SIAM Journal on Computing
Göös, M., Jain, R., & Watson, T. (2018). Extension complexity of independent set polytopes. SIAM Journal on Computing, 47 (1), 241-269. https://doi.org/10.1137/16M109884X